Compensated sigma from measurements made by a pulsed neutron instrument

ABSTRACT

A method for determining a formation thermal neutron decay rate from measurements of radiation resulting from at least one burst of high energy neutrons into formations surrounding a wellbore includes determining a first apparent neutron decay rate in a time window beginning at a first selected time after an end of the at least one burst, a second apparent decay rate from a time window beginning at a second selected time after the burst and a third apparent decay rate from a third selected time after the burst. The second time is later than the first time. A thermal neutron capture cross section of fluid in the wellbore is determined. A decay rate correction factor is determined based on the first and second apparent decay rates and a parameter indicative of the wellbore capture cross-section. The correction factor is applied to the third apparent decay rate to determine the formation thermal neutron decay rate.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a Continuation of U.S. patent application Ser. No.14/424,396, filed Feb. 26, 2015, which is a 371 of InternationalApplication No. PCT/US2013/058131, filed Sep. 5, 2013, which claimsbenefit of U.S. Provisional Patent Application Ser. No. 61/697,178,filed Sep. 5, 2012. Each of the aforementioned related patentapplications is herein incorporated by reference.

BACKGROUND

This disclosure relates generally to the field of pulsed neutron welllogging instruments. More specifically, the disclosure relates tomethods for obtaining values of compensated neutron capture crosssection (sigma) from such instruments.

Formation neutron capture cross section (sigma) measurement based onmeasurements from a pulsed neutron well logging instrument havingcapture gamma ray detectors disposed at axially spaced apart locationsfrom a pulsed neutron generator (PNG) has been used in the oil and gasexploration and production industry for several decades. Suchmeasurements may be referred to as “thermal neutron die-awaymeasurements”, and they are related to the determination of themacroscopic thermal neutron capture cross section of the formation. Thedecay of the thermal neutron population after a “burst” of high energy(in the one million electron volt and above energy range) neutrons fromthe PNG is close to exponential in an ideal situation (for example, ahomogeneous uniform medium surrounding the measuring instrument), whilethe actual neutron population decay cannot be represented by an analyticformula. An apparent decay constant (based on either a curve fitting ormoments method) is not always representative of the “intrinsic”formation “decay constant”, which is inversely proportional to themacroscopic thermal neutron capture cross section (sigma) of theformation surrounding a wellbore from within which measurements areusually made. Wellbore decay contamination of the measured neutronpopulation and thermal neutron diffusion affect the apparent decayconstant. Under some conditions, for example, salty (i.e., high chloridecontent) fluid in the wellbore and values of sigma of the formation muchsmaller than sigma of the wellbore fluid, at least two decay constantscan be observed in the measured neutron population with respect to timefrom the end of a neutron burst, and the decay of the thermal neutronpopulation is very close to a dual exponential decay. However, such dualexponential decay is not always clearly identifiable in the neutronpopulation data. An accurate and precise formation sigma determinationfrom pulsed neutron capture measurements under substantially allconditions and with minimal correction for the wellbore environment is achallenging technical problem.

SUMMARY

A method according to one aspect for determining a formation thermalneutron decay rate from measurements of at least one of thermal neutronsand capture gamma rays resulting from imparting at least one controlledduration burst of high energy neutrons into formations surrounding awellbore includes determining a first apparent decay rate of thermalneutrons in a time window beginning at a first selected time after anend of the at least one burst. A second apparent decay rate of thermalneutrons is determined in a time window beginning at a second selectedtime after the end of the at least one burst. The second selected timeis later than the first selected time. A third apparent decay rate ofthermal neutrons is determined in a time window beginning at a thirdselected time after the end of the at least one burst. A thermal neutroncapture cross section of fluid in the wellbore is determined. A decayrate correction factor is determined based on the first and secondapparent decay rates and a parameter indicative of the wellbore capturecross section. The decay rate correction factor is applied to the thirdapparent decay rate to determine the formation thermal neutron decayrate.

Other aspects and advantages will be apparent from the description andclaims which follow.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows an example wireline conveyed pulsed neutron well logginginstrument.

FIG. 2 shows a while drilling pulsed neutron well logging instrument.

FIG. 3 shows a typical neutron pulsing scheme and neutron populationduring and after each neutron pulse or burst.

FIGS. 4A and 4B show a formation sigma measurement from an apparentsigma with a linear correction term based on the apparent sigma itselffor a fresh water filled wellbore and a wellbore filled with 250 kppmsalt water.

FIGS. 5A and 5B show two apparent taus with two different starting timesversus the true formation tau: one apparent tau is determined startingright after the end of the neutron burst (FIG. 5A), the other starts 130μs after the end of neutron burst FIG. 5B.

FIGS. 6A and 6B show the difference between the true tau and an apparenttau (correction term for the apparent) versus the difference between theearly and late tau. The timing gates used in the early and late tau arethe same as the ones in FIGS. 5A and 5B.

FIGS. 7A and 7B shows how well the tau correction term can be predictedbased on the difference between late and early tau.

FIG. 8 graphically shows the difference between the true tau andapparent tau versus the tau ratio, which is equal to the ratio between anear and far detector apparent tau.

FIG. 9 shows a flow chart of implementing an example method.

FIGS. 10A and 10B show simulation results similar to those in FIGS. 6Aand 6B using a wellbore with different diameter and a casing withdifferent size, therein.

DETAILED DESCRIPTION

FIG. 1 shows an example apparatus for evaluating subsurface formations131 traversed by a wellbore 132. The wellbore 132 is typically, but notnecessarily filled with a drilling fluid or “drilling mud” whichcontains finely divided solids in suspension. Deposits of mud solids maydeposit on the walls of permeable formations in the wellbore 132 to formmudcake 106. A pulsed neutron logging instrument 130 may be suspended inthe wellbore 32 on an armored electrical cable 133, the length of whichsubstantially determines the relative depth of the instrument 130. As isknown in the art, this type of instrument can also operate in a wellhaving casing or tubing inserted therein. The length of cable 133 iscontrolled by suitable means at the surface such as a drum and winchmechanism 134. The depth of the instrument 130 within the wellbore 132can be measured by encoders in an associated sheave wheel 133, whereinthe double-headed arrow represents communication of the depth levelinformation to the surface equipment. Surface equipment, represented at107, can be of conventional type, and can include a processor subsystemand recorder, and communicates with the all the downhole equipment. Itwill be understood that processing can be performed downhole and/or atthe surface, and that some of the processing may be performed at aremote location. Although the instrument 130 is shown as a single body,the instrument 130 may alternatively comprise separate components suchas a cartridge, sonde or skid, and the tool may be combinable with otherlogging tools. The pulsed neutron well logging instrument 130 may, in aform hereof, be of a general type described for example, in U.S. Pat.No. 5,699,246. The instrument 130 may include a housing 111 in the shapeof a cylindrical sleeve, which is capable, for example, of running inopen wellbore, cased wellbore or production tubing. Although notillustrated in FIG. 1, the instrument 130 may also have an eccenteringdevice, for forcing the instrument 130 against the wall of an openwellbore or against wellbore casing. At least one pulsed neutrongenerator (PNG) 115 may be mounted in the housing 111 with a near-spacedradiation detector 116 and a far-spaced radiation detector 117 mountedlongitudinally above the PNG 115, each at a separate axial distancetherefrom. One or more further detectors (not shown) can also beprovided, it being understood that when the near and far detectors arereferenced, use of further detectors can, whenever suitable, be includedas well. Also, it can be noted that a single radiation detector could beused. Acquisition, control, and telemetry electronics 118 serves, amongother functions, to control the timing of burst cycles of the PNG 115,the timing of detection time gates for the near 116 and far 117radiation detectors and to telemeter count rate and other data using thecable 133 and surface telemetry circuitry, which can be part of thesurface instrumentation 107. The surface processor of surfaceinstrumentation 107 can, for example, receive detected thermal neutroncounts, detected epithermal neutron counts and/or gamma ray spectraldata from near and far radiation detectors 116 and 117. The signals canbe recorded as a “log” representing measured parameters with respect todepth or time on, for example, a recorder in the surface instrumentation107. The radiation detectors may include one or more of the followingtypes of radiation detectors, thermal neutron detectors (e.g., ³Heproportional counters), epithermal neutron detectors and scintillationcounters (which may or may not be used in connection with a spectralanalyzer).

The foregoing well logging components can also be used, for example, inlogging-while-drilling (“LWD”) equipment. As shown, for example, in FIG.2, a platform and derrick 210 are positioned over a wellbore 212 thatmay be formed in the Earth by rotary drilling. A drill string 214 may besuspended within the wellbore and may include a drill bit 216 attachedthereto and rotated by a rotary table 218 (energized by means not shown)which engages a kelly 220 at the upper end of the drill string 214. Thedrill string 214 is typically suspended from a hook 222 attached to atraveling block (not shown). The kelly 220 may be connected to the hook222 through a rotary swivel 224 which permits rotation of the drillstring 214 relative to the hook 222. Alternatively, the drill string 214and drill bit 216 may be rotated from the surface by a “top drive” typeof drilling rig.

Drilling fluid or mud 226 is contained in a mud pit 228 adjacent to thederrick 210. A pump 230 pumps the drilling fluid 226 into the drillstring 214 via a port in the swivel 224 to flow downward (as indicatedby the flow arrow 232) through the center of the drill string 214. Thedrilling fluid exits the drill string via ports in the drill bit 216 andthen circulates upward in the annular space between the outside of thedrill string 214 and the wall of the wellbore 212, as indicated by theflow arrows 234. The drilling fluid 226 thereby lubricates the bit andcarries formation cuttings to the surface of the earth. At the surface,the drilling fluid is returned to the mud pit 228 for recirculation. Ifdesired, a directional drilling assembly (not shown) could also beemployed.

A bottom hole assembly (“BHA”) 236 may be mounted within the drillstring 214, preferably near the drill bit 216. The BHA 236 may includesubassemblies for making measurements, processing and storinginformation and for communicating with the Earth's surface. The bottomhole assembly is typically located within several drill collar lengthsof the drill bit 216. In the illustrated BHA 236, a stabilizer collarsection 238 is shown disposed immediately above the drill bit 216,followed in the upward direction by a drill collar section 240, anotherstabilizer collar section 242 and another drill collar section 244. Thisarrangement of drill collar sections and stabilizer collar sections isillustrative only, and other arrangements of components in anyimplementation of the BHA 236 may be used. The need for or desirabilityof the stabilizer collars will depend on drilling conditions.

In the arrangement shown in FIG. 2, the components of a downhole pulsedneutron measurement subassembly that may be located in the drill collarsection 240 above the stabilizer collar 238. Such components could, ifdesired, be located closer to or farther from the drill bit 216, suchas, for example, in either stabilizer collar section 238 or 242 or thedrill collar section 244. The drill collar section 240 may include oneor more radiation detectors (not shown in FIG. 2) substantially asexplained with reference to FIG. 1.

The BHA 236 may also include a telemetry subassembly (not shown) fordata and control communication with the Earth's surface. Such telemetrysubassembly may be of any suitable type, e.g., a mud pulse (pressure oracoustic) telemetry system, wired drill pipe, etc., which receivesoutput signals from LWD measuring instruments in the BHA 236 (includingthe one or more radiation detectors) and transmits encoded signalsrepresentative of such outputs to the surface where the signals aredetected, decoded in a receiver subsystem 246, and applied to aprocessor 248 and/or a recorder 250. The processor 248 may comprise, forexample, a suitably programmed general or special purpose processor. Asurface transmitter subsystem 252 may also be provided for establishingdownward communication with the bottom hole assembly 236. The recorder250 may include devices for recording and/or displaying data acquired bythe instruments in the wellbore and data processed as will be explainedbelow.

The BHA 236 may also include conventional acquisition and processingelectronics (not shown) comprising a microprocessor system (withassociated memory, clock and timing circuitry, and interface circuitry)capable of timing the operation of the accelerator and the datameasuring sensors, storing data from the measuring sensors, processingthe data and storing the results, and coupling any desired portion ofthe data to the telemetry components for transmission to the surface.Alternatively, the data may be stored downhole and retrieved at thesurface upon removal of the drill string. Power for the LWDinstrumentation may be provided by battery or, as known in the art, by aturbine generator disposed in the BHA 236 and powered by the flow ofdrilling fluid.

While the illustrated examples in FIGS. 1 and 2 show a wellbore thatdoes not include a pipe or casing therein (in “open hole”), it is withinthe scope of the present disclosure for the well logging instrument tobe used in wellbores having pipe or casing therein (“cased hole”).

Having shown example instruments for making measurements to be used inembodiments of a method for determining sigma, examples of such methodswill now be explained. A typical neutron pulsing scheme and neutronpopulation is shown in FIG. 3. The neutron generator is repeatedlyturned on for a certain period and then off for another period. Theexample in FIG. 3 has a 240 microsecond (μs) long burst “on” time, shownby neutron burst 302 and an almost 1 millisecond long after-burst “off”time. The time decay spectrum, shown at curve 304, during theafter-burst off time corresponds to thermal neutron decay, which can beused to measure formation sigma. The neutron burst pulsing scheme may bedifferent from the present example (e.g., “dual burst” as explained inU.S. Pat. No. 4,926,044; “multi-burst” as explained in U.S. Pat. No.6,703,606). As long as a neutron measurement decay curve, e.g., at 304,is available it may be used for the formation sigma measurement. Thedetector(s) (see FIG. 1) in the present example may bescintillation-type gamma ray detectors, which measure the gamma raysinduced by thermal neutron capture during the after-burst off time.Measurement of such gamma rays is an indirect measurement of the thermalneutron population around the well logging instrument. The principle ofthe present example may also be applied to thermal neutron detectors(e.g., ³He proportional counters as explained with reference to FIGS. 1and 2). The use of one or more gamma ray detectors may be preferred overusing thermal neutron detectors due to their higher count rates andassociated better statistical precision..

In some examples, one may use the moments method to compute the apparentdecay constant from a count rate curve such as 304 in FIG. 3. If thedecay curve has a single exponential decay constant, the first ordermoment is equal to the decay constant, as shown in Equation 1.

$\begin{matrix}{x = \frac{\int_{0}^{\infty}{t \cdot e^{- \frac{t}{x}} \cdot {dt}}}{\int_{0}^{\infty}{e^{- \frac{t}{x}} \cdot {dt}}}} & (1)\end{matrix}$

In Equation 1, x is the exponential decay constant and t is the timevariable. As a practical matter, the decay curve is not single decayconstant exponential curve. The decay curve is not measured up toinfinite time from the end of the neutron bursts, but can only bemeasured during a finite time range. Equation 2 may be used to computethe first order moment, τ₁.

$\begin{matrix}{\tau_{1} = \frac{{\int_{t_{0}}^{T}( {t - t_{0}} )}{\cdot {f(t)} \cdot {dt}}}{\int_{t_{0}}^{T}{{f(t)} \cdot {dt}}}} & (2)\end{matrix}$

In Equation 2, f(t) is the measured decay curve (time spectrum of thedetector count rate), t₀ is the starting time of the moment and T is thestop time of the moment. Because the integral in Equation 2 is not takenfrom zero to infinity, even if f(t) were a perfect exponential decaycurve, τ₁ is not equal to the decay constant of such curve. In order tomake them equal, one may perform a correction for the finite integral,which is shown in Equation 3.

$\begin{matrix}{{Finite\_ corr} = {1 - {8 \cdot ( \frac{T - t_{0}}{\tau_{1}} )^{3}}}} & (3)\end{matrix}$

The correction provided by Equation 3 is an approximation. A theoreticalcorrection may be provided in other examples by iterative methods. Theapparent thermal neutron decay rate [tau (τ)] then can be computed asthe ratio of τ₁ and the finite integral correction term, as shown inEquation 4.

$\begin{matrix}{\tau = \frac{\tau_{1}}{Finite\_ corr}} & (4)\end{matrix}$

The apparent sigma (Σ) can be computed using Equation 5.

$\begin{matrix}{\Sigma = \frac{4545}{\tau}} & (5)\end{matrix}$

The apparent tau is a function of the starting time (t₀) and end time(T) of the time interval (gate) used in the foregoing integralequations. Varying the starting time will not only change the wellboreand diffusion effect in the apparent tau, but will also change thestatistical precision. An apparent tau computed using the aboveequations and with an early starting time may be expected to have morewellbore and diffusion effect than one with a later starting time,because, as explained above, wellbore decay and diffusion typicallyoccur early after the end of the neutron burst and formation decay tendsto occur at later times after the end of the neutron burst. Varying thegate end time will only change the statistical precision due to thepresence of activation background radiation, which should be subtractedfrom the overall count rate data before determining the decay constant.

It is known in the art to optimize the timing gate (both starting timeand end time) to achieve better precision and reduce the wellborecontamination and diffusion effect. However, the wellbore contaminationand diffusion effect cannot be eliminated by only optimizing the timinggate. A feature of the present example includes computing two (or more)apparent decay constants based on different timing gates andcompensating the wellbore and diffusion effects completely.

FIGS. 4A and 4B show, respectively, two cross-plots of the apparentsigma with respect to the true formation sigma in various formationconditions and wellbore conditions (e.g., connate fluid salinity, andformation porosity and lithology). The apparent sigma is based on atiming gate starting 130 μs after the end of the neutron burst using thepulsing scheme shown in FIG. 3. The data were computed using a MonteCarlo method (MCNP) in a simulated 12 inch diameter wellbore with a9.625 inch outer diameter (OD) casing disposed in the example wellbore.The casing inner diameter (ID) was 8.535 inches. FIG. 4A shows theresults for a fresh water wellbore, and FIG. 4B shows results for a saltwater (250 ppk) filled wellbore. Thirty six different formations weremodeled: sandstone, limestone and dolomite with 0-p.u. (p.u. represents“porosity units” or percent porosity), 2.5-p.u., 5-p.u., 10-p.u.,20-p.u., and 40-p.u. fresh water; sandstone 10-p.u., 20-p.u., 40-p.u.and 60-p.u. salt water (100 ppk, 200 ppk and 260 ppk); 0-p.u. anhydrite,H&H shale (dry clay based on core sample analysis), 10% dry clay plus90% sand, 20% dry clay plus 80% sand, and 100-p.u. fresh water.

As shown in FIG. 4A, in the fresh water-filled wellbore, the apparentsigma is approximately equal to a constant plus the true sigma when thetrue sigma is less than about 25 capture units (c.u.). When the truesigma is more than 25 c.u., the apparent sigma becomes saturated anddramatically diverges from the true sigma. The foregoing is indicated bydata point deviation from line 400. The foregoing deviation is caused bythe fact that the formation sigma is higher than the wellbore sigma. Inthis case, the formation decay is fast and occurs early, while thewellbore decay is slow and occurs late. A relatively late gate startingtime (130 μs) does not effectively measure the formation decay, butmeasures the wellbore decay plus the effect of neutron diffusion fromthe wellbore to the formation, giving erroneous values of tau. This isthe so-called “crossover” condition, which in the present context meansthe formation and wellbore decay cross over in apparent decay time. Inthe salt water-filled wellbore, as shown in FIG. 4B, the apparent sigmais well-ordered and almost equal to a constant plus the true sigma, asshown by the data points closely following line 402. There are fewcrossover conditions because the wellbore sigma is higher than theformation sigma. It should be noted that there is not a cleardistinction between crossover and non-crossover conditions.

In non-crossover conditions, the correction for the apparent sigma issmall (within 5 c.u.). Therefore, it is relatively easy to have aformation sigma measurement from the apparent sigma with a linearcorrection term based on the apparent sigma itself. However, such linearcorrection will not be exact. For example, 0-p.u. anhydrite will have a3 to 4 c.u. error, and 0-p.u. sandstone will have a 2 to 3 c.u. error,as shown in FIG. 4B. Such errors are a function of lithology (formationmineral composition) and porosity. Although the values of these errorsare not very large in absolute terms, they are very large in percentageterms (up to 50% for 0-p.u. sandstone). Thus, it is difficult to have anaccurate formation sigma measurement with an error smaller than 1 c.u.that is independent of lithology and porosity. Another difficulty is thepresence of the crossover condition.

In order to overcome the two difficulties described above, the presentexample provides a method to compensate the apparent tau using thedifference between two apparent taus, each computed from a measurementgate having a different starting time from the end of the neutron burst.FIGS. 5A and 5B show two apparent taus with two different gate startingtimes with respect to the true formation tau: one apparent tau isdetermined using a timing gate starting at the end of the neutron burst(early tau, FIG. 5A), the other uses a timing gate starting 130 μs afterthe end of neutron burst (late tau, FIG. 5B). The wellbore and formationconditions are the same as those used to generate the data shown inFIGS. 4A and 4B, except that the wellbore fluid for both FIGS. 5A and 5Bis fresh water. The apparent and true tau in FIG. 5B can be converted tothe apparent and true sigma in FIG. 4A using Equation 5. The percentagecorrection for apparent tau is the same as the percentage correction forthe apparent sigma, but the absolute corrections are quite different.For example, the 0-p.u. sandstone has the largest tau (1000 μs) andsmallest sigma (4.55 c.u.). The difference between the true tau andapparent tau is 600 μs for the late tau, and the difference between thetrue sigma and the apparent sigma is 6.8 c.u.

As can be observed in FIG. 5A and 5B, there are lithology effects in theapparent tau, particularly for high tau values (low sigma values). Forexample, fresh water filled limestone with porosity lower than 5 p.u.will not be on the same line as sandstone or dolomite. Another exampleis 0-p.u. anhydrite. In addition, the apparent tau does notmonotonically increase with respect to the true tau. Above 500 μs, theapparent tau can drop (depending on lithology and porosity) withincreasing true tau. The correction should take this fact into accountin order to obtain good accuracy. Both the early and late tau havesimilar lithology effects and behave similarly with respect tolithology. However, there are differences between the two. The late tauis closer to the true tau than the early tau. The difference between theearly and late values of tau may be used to compensate the apparent tauin order to compute the true tau.

FIG. 6A and 6B show the difference between the true tau and a thirdapparent tau with respect to the difference between the early (first)and late (second) tau (At). The timing gates used in the early and latetau are the same as the ones shown in FIGS. 5A and 5B. The thirdapparent tau to which a “tau correction” (or compensation, explainedbelow) may be applied can be computed based on any timing gate, while inthe present case it may be the same as the late tau. The wellbore andformation conditions are the same as ones used to generate the datashown in FIGS. 4A and 4B. As can be observed in FIG. 6A, the correctionterm for the apparent tau can be predicted very well based on a secondorder polynomial fit, indicated by curves 602 and 604, for non-crossoverconditions if the wellbore fluid is known. Here one may define thecrossover condition as when the difference between the true tau and theapparent tau is less than zero. FIG. 6A shows that the polynomial fit,curve 604 does not predict the data points below zero at all. Recallthat in crossover conditions the wellbore decay occurs late while theformation decay occurs early. Thus, one may compute Δτ to be the latetau minus the early tau in non-crossover conditions, and in crossoverconditions Δτ is equal to the early tau minus the late tau. One may plotthe difference, either visually on a display or printed graph or in theprocessor (see FIG. 2) between true tau and apparent tau versus Δτ inFIG. 6B. As can be observed at curves 606 and 608, the polynomial fitdetermined from the foregoing simulations can be used to predict acorrection term very well for a wide range of wellbore and formationconditions. The foregoing correction may be referred to as the “taucorrection.” The tau correction is substantially independent oflithology and porosity. The tau correction may be implemented, forexample, using a predetermined polynomial expression or a lookup table.Other implementations will occur to those skilled in the art. In thepresent example, the value of the tau correction is related to thearithmetic difference between the late tau and the early tau, howeverfor purposes of defining the scope of the disclosure, any relationshipthat depends on the values of early tau and late tau may be used, forexample and without limitation, a ratio of early tau to late tau (or itsinverse), difference between logarithms of the two tau values anddifference between the tau values wherein each tau value is multipliedby a corresponding constant.

The selection of the timing gates for the three apparent taus representsa trade-off between accuracy and precision. Generally speaking, oneshould select the early timing gate for the early tau as early aspossible (e.g., at the end of the neutron burst) and the late timinggate for the late tau as late as possible to minimize the correlationbetween the two. The smaller the correction is, the better the accuracyand precision of the tau correction are. The earliest timing gate isright after the neutron burst, which also gives the best precision forthe apparent tau because it is using all the data in the decay curve. Onthe other hand, the precision of the apparent tau will degrade as thetiming gate becomes later because it is using less data in the decaycurve. The selection of the third timing gate for the third apparent taucan be optimized. An early timing gate will give better precision forthe third apparent tau, but it requires a larger tau correction term toobtain the true formation tau, which is not preferred in term ofaccuracy. A late timing gate will require a smaller tau correction term,however, it will provide lower statistical precision for the thirdapparent tau.

To illustrate the tau correction in a wellbore which has a differentconfiguration (such as wellbore diameter or casing size) than the oneused in FIGS. 6A and 6B, FIGS. 10A and 10B show the modeling results ina 8-inch wellbore with a 5.5-inch OD casing (4.94-inch ID). Since thewellbore effects and diffusion effects in different wellboreconfigurations are different, the function which may be used todetermine tau correction based on Δτ becomes different. However, thegeneral formula may still be the same, which in the present example is asecond order polynomial fit, indicated by the solid lines 1000 and 1002in FIG. 10A and 1004 and 1006 in FIG. 10B. The only thing changed fromone wellbore configuration to another are the coefficients of thepolynomial function. Therefore, one can calibrate the coefficients invarious wellbore configurations and then determine the coefficients forany wellbore configuration based on the calibrated ones by, e.g.,interpolation, lookup table, or an analytic function.

A more detailed inspection of FIGS. 6A, 6B, 10A and 10B shows that thecurve for high wellbore salinity is almost unaffected by the change inwellbore size, while the curve for the fresh water-filled wellbore hasmoved much closer to the 250-ppk curve. This illustrates that theprincipal effects of casing and cement results from the wellbore fluid.Reducing the volume of the wellbore fluid in smaller casing leads to acorresponding, and frequently large reduction in the wellbore fluideffect. It may therefore be possible to use a simple analytic functionto describe the magnitude of the correction as a function of thewellbore parameters. In the case of high wellbore salinity thecorrection may be substantially independent of the wellbore geometry.

The foregoing modeling results used to verify the functionality of thepresent example method were based on a wellbore having a casing therein,as explained with reference to FIGS. 4A and 4B. It should be clearlyunderstood that the present example method may be equally useful inwellbores having no casing therein (“open hole”). The presence orabsence of casing is not a limitation on the scope of the disclosure.

It should be noted that the tau correction may introduce somestatistical noise in the results. Because the tau correction amplitudecan be quite large compared to Δτ, the noise in Δτ then will bemagnified after the correction. A possible solution for the foregoing isto apply an adaptive filter to the tau correction term. Testing showedthat in general a 5-level (depth or axial position increment) adaptivefilter may be sufficient. Such a filter is not expected to degrade theaxial resolution of the measurement to any substantial degree.

There are two data that need to be known in order to perform the abovedescribed correction. One datum is the wellbore fluid composition, theother is whether the condition at the position of measurement iscrossover or not. In a liquid-filled wellbore (oil or water), themeasured wellbore fluid sigma can be used to compute the tau correction.The value wellbore fluid sigma need not be known or determined veryaccurately. Experiments verified that the sigma accuracy based on thismethod can be within 1 c.u. using a wellbore sigma value with anuncertainty (1 standard deviation) of about 10 c.u. for non-crossoverconditions. The crossover condition requires a wellbore sigmameasurement with better accuracy than 10 c.u., and in such cases it maybe desirable to measure wellbore fluid sigma There are different ways tomeasure the wellbore fluid sigma, for example, based on the “dual-burst”model as explained in U.S. Pat. No. 4,926,044. The wellbore fluid sigmacan also be determined by a resistivity measurement made on a fluidsample at the surface, or made in the wellbore. The wellbore measurementmay be preferably made at the time of the pulsed neutron dataacquisition.

A tau correction plot similar to FIGS. 6A and 6B is shown in FIGS. 7Aand 7B. All the apparent decay constants (tau) are computed based on asingle exponential fit in various timing gates, which are the same asthe timing used to generate the plots shown in FIGS. 6A and 6B. Thedifferences between FIGS. 6A, 6B and FIG. 7A, 7B are due to thedifferent wellbore and diffusion effects on the apparent decayconstants, which are computed using the two different above describedapproaches. However, the same method used in the present example can beused to compensate the apparent tau for both. The solid lines in FIGS.7A and 7B, 702, 704, 706, 708 show how well the tau correction term canbe predicted based on the difference between late and early tau. Thisexample indicates the principle of the present example can be applied tothe computed apparent decay constants using any method. A comparison ofthe results of FIGS. 6A, 6B, to those shown in FIGS. 7A and 7B indicatesthat in the latter case there is a smaller effect of the wellbore fluidsalinity. Therefore, the determination of wellbore sigma can be lessaccurate without affecting the accuracy of the final answer.

In order to know whether the existing condition is crossover or not, acrossover indicator may be used, which is related to the ratio betweenthe apparent tau from a near spacing detector and the apparent tau froma far spacing detector (see FIG. 1). This crossover indicator only worksfor a well logging instrument with two or more detectors with differentaxial spacings from the neutron source. FIG. 8 shows the differencebetween the true tau and apparent tau versus the tau ratio, which isequal to the ratio between the near and far detector apparent tau. Inthis case, the timing gate used in the apparent tau computation is thesame as the one for the late tau. However, similar performance can beobtained using other timing gates. The wellbore and formation conditionsare the same as the ones used to generate the data shown in FIGS. 4A and4B, except that there are 6 different wellbore fluids (0 ppk, 50 ppk,100 ppk, 150 ppk, 200 ppk and 250 ppk sodium chloride concentration inwater). As can be observed in FIG. 8, almost all the crossoverconditions (below zero) correspond to a tau ratio larger than around0.96, and almost all non-crossover conditions (above zero) correspond toa tau ratio less than 0.96. Thus, the tau ratio can be used as acrossover indicator to determine the sign of Δτ. Additional informationcan also be used to make the tau ratio a more robust crossoverindicator. For example, it is known that crossover means that formationsigma is high and wellbore sigma is low, one may use the apparentformation sigma and wellbore sigma to determine the crossover condition,or to make the tau ratio a more robust indicator.

FIG. 9 shows a flow chart of the present example method. At 900, theearly tau may be computed using the moment method. At 902, a late tauvalue may be computed using the moment method. At 904, Δτ is computed,which is equal to late tau minus early tau. At 906, based on thecrossover indicator, determine whether the current condition iscrossover. If yes, at 908, make Δτ negative of its present value. Ifnot, take no action. At 912, obtain a wellbore sigma measurement. At910, use the wellbore sigma and Δτ to compute the tau correction. At914, an adaptive filter may be applied to the tau correction term. At916, the third apparent tau is computed. The formation tau is computedas the sum of the tau correction and the third apparent tau. At 918, onemay compute the formation sigma from the formation tau.

Because sigma and tau can be converted to each other using Equation 5,following the same principle as the described example method, one canreadily perform the above described correction in the sigma domaininstead of the tau domain. Thus for purposes of defining the scope ofthe present disclosure, any reference to thermal neutron decay rate maybe substituted by a corresponding thermal neutron capture cross section.

While the invention has been described with respect to a limited numberof embodiments, those skilled in the art, having benefit of thisdisclosure, will appreciate that other embodiments can be devised whichdo not depart from the scope of the invention as disclosed herein.Accordingly, the scope of the invention should be limited only by theattached claims.

What is claimed is:
 1. A method, comprising: moving a pulsed neutronlogging instrument in a wellbore; imparting at least one controlledduration burst of high energy neutrons into formations surrounding thewellbore; measuring at least one of thermal neutrons and capture gammarays resulting from said imparting; in a processor, determining a firstapparent decay rate of thermal neutrons in a time window beginning at afirst selected time after an end of the at least one burst; in theprocessor, determining a second apparent decay rate of thermal neutronsin a time window beginning at a second selected time after an end of theat least one burst, the second selected time being later than the firstselected time; in the processor, determining a third apparent decay rateof thermal neutrons in a time window beginning at a third selected timeafter an end of the at least one burst; in the processor, determining adecay rate correction factor based on the first and second decay ratesand a parameter indicative of the wellbore thermal neutron capture crosssection; and in the processor applying the decay rate correction factorto the third apparent decay rate to determine the formation thermalneutron decay rate.
 2. The method of claim 1 further comprisingdetermining a formation thermal neutron capture cross section from theformation thermal neutron decay rate.
 3. The method of claim 1 whereinthe first apparent decay rate, the second apparent decay rate, and thethird apparent decay rate are determined from radiation detector countrates by a moment method.
 4. The method of claim 3 wherein the radiationdetector comprises at least one of a gamma ray detector and a thermalneutron detector.
 5. The method of claim 1 wherein the correction factoris based on an arithmetic difference between the first and second decayrates.
 6. The method of claim 5 further comprising determining when acrossover condition exists and inverting a sign of the apparent decayrate difference when the crossover condition exists.
 7. The method ofclaim 6 wherein the determining when a crossover condition existscomprises determining a ratio of an apparent thermal neutron decay ratebased on the first radiation detector and a corresponding thermalneutron decay rate from measurements made by the second radiationdetector which has a different spacing from a position of imparting theburst of neutrons than the first radiation detector, the crossovercondition determined to exist when the ratio exceeds a selectedthreshold.
 8. The method of claim 6 wherein the determining when acrossover condition exists is done by comparing an apparent formationsigma with the wellbore thermal neutron capture cross section.
 9. Themethod of claim 1 further comprising adaptively filtering the determineddecay rate correction factor.
 10. The method of claim 1 wherein theparameter indicative of wellbore fluid thermal neutron capture crosssection is determined by making a thermal neutron decay rate measurementof the fluid in the wellbore.
 11. The method of claim 1 wherein theparameter indicative of wellbore fluid thermal neutron capture crosssection is determined by measuring a resistivity of the fluid.
 12. Themethod of claim 1 wherein the third selected time is the same as thefirst or second selected time.
 13. The method of claim 1 wherein thethird selected time is the same as the second selected time.
 14. Amethod for well logging, comprising: moving a well logging instrumentalong an interior of a wellbore drilled through subsurface formations,the instrument including a pulsed neutron source and at least oneradiation detector disposed at an axially spaced apart position from thepulsed neutron source; operating the pulsed neutron source to emit atleast one controlled duration burst of neutrons into the wellbore andthe formations; detecting radiation related to thermal neutronpopulation using the radiation detector after an end of the at least oneburst; in a processor, determining a first apparent decay rate ofthermal neutrons in a time window beginning at a first selected timeafter an end of the at least one burst; in the processor, determining asecond apparent decay rate of thermal neutrons in a time windowbeginning at a second selected time after an end of the at least oneburst, the second selected time being later than the first selectedtime; in the processor, determining a third apparent decay rate ofthermal neutrons in a time window beginning at a third selected timeafter an end of the at least one burst; in the processor, determining athermal neutron capture cross section of fluid in the wellbore; in theprocessor, determining a decay rate correction factor based on the firstand second apparent decay rates and the wellbore capture cross-section;and in the processor applying the correction factor to the thirdapparent decay rate to determine the formation thermal neutron decayrate.
 15. The method of claim 14 further comprising determining aformation thermal neutron capture cross section from the formationthermal neutron decay rate.
 16. The method of claim 14 wherein thefirst, second and third apparent decay rates are determined fromradiation detector count rates by a moment method.
 17. The method ofclaim 14 wherein the radiation detector comprises at least one of agamma ray detector and a thermal neutron detector.
 18. The method ofclaim 14 wherein the correction factor is based on an arithmeticdifference between the first and second apparent decay rates.
 19. Themethod of claim 18 further comprising determining when a crossovercondition exists and inverting a sign of the apparent decay ratedifference when the crossover condition exists.
 20. The method of claim19 wherein the determining when a crossover condition exists comprisesdetermining a ratio of the second apparent thermal neutron decay rateand a corresponding thermal neutron decay rate from measurements made bya radiation detector having a different spacing from a position ofimparting the burst of neutrons than a radiation detector used todetermine the second apparent thermal neutron decay rate, the crossovercondition determined to exist when the ratio exceeds a selectedthreshold.
 21. The method of claim 19 wherein the determining when acrossover condition exists by comparing an apparent formation sigma withthe wellbore thermal neutron capture cross section.
 22. The method ofclaim 14 further comprising adaptively filtering the determined decayrate correction factor.
 23. The method of claim 14 wherein the wellborefluid capture cross section is determined by making a thermal neutrondecay rate measurement of the fluid in the wellbore.
 24. The method ofclaim 14 wherein the wellbore fluid capture cross section is determinedby measuring a resistivity of the fluid.